The motivation behind the collection of papers presented in this THEORIA forum on Abductive reasoning is my book Abductive Reasoning: Logical Investigations into the Processes of Discovery and Explanation. These contributions raise fundamental questions. One of them concerns the conjectural character of abduction. The choice of a logical framework for abduction is also discussed in detail, both its inferential aspect and search strategies. Abduction is also analyzed as inference to the best explanation, as well as a process of epistemic change, both of which chal-lenge the argument-like format of abduction. Finally, the psychological question of whether humans reason abduc-tively according to the models proposed is also addressed. I offer a brief summary of my book and then comment on and respond to several challenges that were posed to my work by the contributors to this issue